Explain why the nature of roots depends on the value of the dicriminant.​

Therefore , the solution of the given problem of equation comes out to be  Y is equally distant from X and Z.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization produces a + 7 as opposed to a different algorithm that splits 12 into two parts and can evaluate data received from x + 7.

Here,

We can infer from the knowledge that

=> PQ = XZ

because X, Y, and Z are equally spaced apart from P and Q.

Based on this knowledge alone, we cannot infer that X, Y, and Z are collinear or that Y is equally distant from X and Z.

Therefore , the solution of the given problem of equation comes out to be  Y is equally distant from X and Z.

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Using Cauchy-Euler equation, the solution of the second-order homogeneous differential equation  is y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x

The given LODE is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is given by:

9r^2 - 6r + 2 = 0

Using the quadratic formula, we find the roots to be:

r = (1/3) ± i/sqrt(3)

Thus, the general solution to the differential equation is:

y(x) = c1 * x^(1/3) * cos((1/3)*arccos(sqrt(3)*r)) + c2 * x^(1/3) * sin((1/3)*arccos(sqrt(3)*r))

To find the first solution, we can choose either the cosine or sine term. Let's choose the cosine term for simplicity:

y1(x) = x^(1/3) * cos((1/3)*arccos(sqrt(3)*r))

To find the second solution, we can use the method of reduction of order. Assume that the second solution has the form:

y2(x) = v(x) * y1(x)

Substituting this into the differential equation, we obtain:

9x^2(v''(x)*y1(x) + 2v'(x)*y1'(x) + v(x)*y1''(x)) - 6x(v'(x)*y1(x) + v(x)*y1'(x)) + 2v(x)*y1(x) = 0

Simplifying this equation by dividing by x^2*y1(x), we get:

9v''(x) + (18/r)x*v'(x) + ((2/r^2) - 1)v(x) = 0

where r = sqrt(3)

This is a Cauchy-Euler equation, which can be solved by assuming a solution of the form:

v(x) = x^m

Substituting this into the equation, we obtain:

9m(m-1) + (18/r)m + ((2/r^2) - 1) = 0

Simplifying this equation, we get:

9m^2 + 6m + 1 = 0

Using the quadratic formula, we find the roots to be:

m = (-1/3) or (-1/3)

Thus, the second solution is given by:

y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * ln(x)

To determine the first four leading terms in the second solution, we can use the Taylor series expansion of the natural logarithm:

ln(x) = (x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...

Substituting this into the second solution, we obtain:

y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * [(x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...]

Simplifying this expression, we get:

y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * (x-1) - c4 * x^(1/6) * (1/2)(x-1)^2 + c4 * x^(1/3) * (1/3)(x-1)^3 - ...

Thus, the first four leading terms in the second solution are:

y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x

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The transformation that it could have been is either a rotation or a reflection, over one of the vertices of the figure.

The possible transformations on a figure are listed as follows:

Either a reflection or a rotation can happen over one of the vertices of the graph, which will keep it's coordinates constant, and thus the transformation in the context of this problem is either one of these two.

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The answer of the given question based on the  number best describes a typical rating in the contest the answer is 7.9.

The median is  measure of central tendency in statistics that represents  middle value of  dataset. It is  value that separates  highest 50% of  values from the lowest 50%.

To find  median of a dataset, you first need to sort  data in ascending or descending order.

The median rating is 7.9, which means that half of the contestants scored above 7.9 and half scored below. This suggests that 7.9 is a representative value of the ratings overall.

Additionally, the interquartile range (IQR) is a measure of the spread of the middle 50% of the ratings, and it is given as 0.8. This means that the ratings between the 25th and 75th percentile fall within a range of 0.8, which suggests that the ratings are fairly tightly clustered around the median of 7.9.

Therefore, the number that best describes a typical rating in the contest is 7.9.

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The width of the rectangular tile is obtained to be 11 and 2/3 cm.

What is a rectangle?

A quadrilateral with parallel sides that are equivalent to one another and four equal vertices is known as a rectangle. It is also known as an equiangular rectangle for this reason.

The bathroom tile is in a rectangular shape.

Let's call the width of the tile "w".

From the problem, we know that -

w = (2 and 1/3) × h

We also know that the height of the tile is 5 cm.

Substituting this value in the equation above, we get -

w = (2 and 1/3) × 5 cm

w = 7/3 × 5 cm

w = 35/3 cm

w = 11 and 2/3 cm

Therefore, the width of the tile is 11 and 2/3 cm.

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The statement that best assesses the linearity of the relationship between age and vertical jump, given that the scatterplot appears to be approximately linear, is:

Although it is given that the scatterplot is reasonably linear, because the residual plot has no obvious pattern, it is appropriate to use the line of best fit to predict vertical jump based on age.

The second option is correct.

What is a  residual plot ?

A  residual plot is described as a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model.

If the residual plot has no obvious pattern, it suggests that the relationship between the variables is linear and that the line of best fit is appropriate for predicting the vertical jump based on age.

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Answer:

thx to the comments

Step-by-step explanation:

Answer: 3a^5b

Step-by-step explanation:

I just did an exam with the question, and I got it correct.

Answer:

Like the other person said, C.

Step-by-step explanation:

also got it correct on the test

have a good day xx

According the question 89+82  expressiοn is the same as 8(9+2).

An expressiοn in math is a sentence with a minimum οf twο numbers οr variables and at least οne math οperatiοn. This math οperatiοn can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn.

Algebraic expressiοns are classified οn the basis οf the number οf terms in the expressiοn. The variοus types οf algebraic expressiοns are:

The difference between expressiοns and equatiοns is that an expressiοn signifies a cοmbinatiοn οf numbers, variables, and οperatiοn symbοls whereas an equatiοn will always use an equal (=) οperatοr between twο math expressiοns.

The expressiοn 8(9+2) can be simplified using the distributive prοperty οf multiplicatiοn οver additiοn:

8(9+2) = 89 + 82

Therefοre, the answer is: 89+82

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The fraction that represents the addition model of part A is 5/10, and for part B is 3/100.

Parts of a whole are defined as fractions. The top and bottom numbers of a fraction are explained in the fundamentals of fractions. The number at the top represents the number of selected pieces of a whole, while the number at the bottom reflects the entire number of components.

According to the given information:

Based on the information provided, a grid A with 10 equal columns is depicted, with 5 shaded in. This will be expressed as a score of 5/10.

A second grid B, same in size, with 100 squares shaded in is also presented. This will be expressed as 3/100.

In this situation, Emma's response is erroneous because he added 5 to 3 and received an 8/100.

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Answer:

Their average velocity during their trip was 59.19 miles per hour.

Step-by-step explanation:

To calculate the average velocity of the family's trip, we divide the total distance traveled by the time it took to travel that distance:

Average velocity = total distance ÷ time

In this case, the total distance traveled is 509 miles and the time it took to travel that distance is 8.6 hours. So, we can plug these values into the formula:

Average velocity = 509 miles ÷ 8.6 hours

Simplifying this equation, we get:

Average velocity = 59.19 miles per hour (rounded to two decimal places)

Therefore, the family's average velocity during their trip was 59.19 miles per hour.

Step-by-step explanation:

Think we can get a better picture, maybe more light? I wouldn't mind helping if you can

The y-intercept of the equation is -10.

Equation is a mathematical statement that expresses the equality of two expressions, which are separated by an equals sign. It can be used to represent a variety of different relationships, such as equality, inequality, addition, subtraction, multiplication, and division. Equations can be used to solve a variety of problems in science, engineering, and mathematics.

The x-intercepts of the graph of the equation r(x) are those values of x for which the equation is equal to 0. To find the x-intercepts, we must solve the equation:

x²+ 3x - 10 = 0

Factoring the equation, we get:

(x+5)(x-3)(x+1) = 0

The solutions of this equation are x = -5, -1, and 3. Therefore, the x-intercepts of the equation are -5, -1, and 3.

To find the y-intercept, we must plug 0 in for x in the equation:

y = x² + 3x - 10/ (x+1)(x-3)(x+5)

When x = 0, we get:

y = -10/ (0+1)(0-3)(0+5)

Therefore, the y-intercept of the equation is -10.

The vertical asymptote of the equation is the line x = -1, since it is the only value of x that makes the denominator equal to 0.

The horizontal asymptote of the equation is the line y = 0, since the degree of the numerator is less than the degree of the denominator.

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The y-intercept of the equation is -10.the x-intercepts of the equation are -5, -1, and 3.

Equation is a mathematical statement that expresses the equality of two expressions, which are separated by an equals sign. It can be used to represent a variety of different relationships, such as equality, inequality, addition, subtraction, multiplication, and division. Equations can be used to solve a variety of problems in science, engineering, and mathematics.

The x-intercepts of the graph of the equation r(x) are those values of x for which the equation is equal to 0. To find the x-intercepts, we must solve the equation:

x²+ 3x - 10 = 0

Factoring the equation, we get:

(x+5)(x-3)(x+1) = 0

The solutions of this equation are x = -5, -1, and 3. Therefore, the x-intercepts of the equation are -5, -1, and 3.

To find the y-intercept, we must plug 0 in for x in the equation:

y = x² + 3x - 10/ (x+1)(x-3)(x+5)

When x = 0, we get:

y = -10/ (0+1)(0-3)(0+5)

Therefore, the y-intercept of the equation is -10.

The vertical asymptote of the equation is the line x = -1, since it is the only value of x that makes the denominator equal to 0.

The horizontal asymptote of the equation is the line y = 0, since the degree of the numerator is less than the degree of the denominator.

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The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.

Spread and distribution of data are statistical concepts that describe how a set of data is spread out or distributed.

Distribution refers to how the data is distributed or arranged. It is typically described in terms of its shape, center, and spread. Common types of distributions include normal distribution, skewed distribution, and uniform distribution. The distribution can be visualized using various graphs such as histograms, box plots, and scatter plots.

Based on the histogram description, the best answer is:

The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.

The histogram shows that the frequency of calls is highest for the 1 to 25 interval, with decreasing frequency for each subsequent interval. The fact that the shaded bars stop at relatively low frequencies for each interval suggests that there are very few patients who call the doctor frequently, skewing the data towards the lower values. The histogram also shows a wide range of values, or spread, with the highest interval going up to 100, but the low frequencies in each interval suggest that the data is not normally distributed.

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Answer:its b

Step-by-step explanation:

Answer:

C) 25

Step-by-step explanation:

A square has all four sides equal.

5x = 10x - 25

-5x = -25

x = 5

Now put 5 in for x, and you get the answer is 25

The expressiοn that tells the weight οf the flοur left in the bag is 2 - 0.25

A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expression or mathematical expression. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression.

Here, we have

Given: From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread.

We have to find the expression that tells the weight of the flour left in the bag.

Marcella took 1/4 pound to bake bread = 0.25

If Marcella took 0.25 pounds from a 2-pound flour bag then she left with 1.75 pounds.

Hence,  the expression that tells the weight of the flour left in the bag is 2 - 0.25

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The image was created by translating 5 units down, 5 units up, 1 unit down, and 1 unit up. ABCD and A'B'C'D' are two polygons on the graph.

The first polygon, ABCD, has vertices at (4,4), (12,4), (8,4), and (1,1),). (3,1). The vertices of the second polygon, A'B'C'D', are located at (1,1), (3,1), (3,2), and (1,2). (0.5,.25).

We can establish the translation that was applied to produce the image by comparing the coordinates of the two polygons. The two polygons' initial coordinate is (1,-1) and their second coordinate is (1,-1). (1,-6). The translation is 5 units lower because of the 5-unit difference in the y-coordinate. The second coordinate for the two polygons is (3,-5) and (3,-10). The translation is 5 units lower because of the 5-unit difference in the y-coordinate.

The third coordinate of the second polygon is (7,-5) and (7,-10). The translation is 5 units lower because of the 5-unit difference in the y-coordinate. The fourth coordinate of both polygons is (5,-1). (5,-6). The translation is 5 units lower because of the 5-unit difference in the y-coordinate.

The translation of the image was five units down, five units up, one unit down, and one unit up.

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Answer: C = 1/4

Step-by-step explanation: I got it right on my test

Hope this helps :)

Step-by-step explanation:

The formula to calculate the circumference of a circle is:

Circumference = 2πr

where "r" is the radius of the circle and "π" is the mathematical constant pi, approximately equal to 3.14159.

Given that the circumference of the circle is 20 ft, we can plug in the values into the formula and solve for "r":

20 = 2πr

Divide both sides of the equation by 2π:

r = 20 / (2π)

Simplify the expression by using the approximation of π as 3.14159:

r = 20 / (2 x 3.14159)

r = 3.1831 ft (rounded to four decimal places)

Therefore, the radius of the circle is approximately 3.1831 feet.

The solution to  4^x = 5^x +^2 is

x = -2log 5/( log 5 - log 4)

Option C is correct.

We will rewrite the equation as:

4^x = 5^x * 5^2

applying  the logarithm function to both sides of the equation.

log(4^x) = log(5^x * 5^2)

simplifying the right side of the equation, using the properties of logarithms,

log(4^x) = log(5^x) + log(5^2)

log(4^x) = xlog(4) = x2log(2)

log(5^x) + log(5^2) = xlog(5) + log(25)

Substituting these results back into the original equation, we have:

x2log(2) = x*log(5) + log(25)

x*(2*log(2) - log(5)) = log(25)

Divide  both sides by (2*log(2) - log(5)), we get:

x = x = -2log 5/( log 5 - log 4)

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Answer:

a= positive

b= When the graph goes up it means it has a positive trend.

c= the direction does not make sense because the measurements for the x and y coordinate do not correlate with each other.

Step-by-step explanation:

Answer:

40 units

Step-by-step explanation:

12+12+8+8=40 units

The cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.

A system οf linear equatiοns can be sοlved graphically, by substitutiοn, by eliminatiοn, and by the use οf matrices.

The cοrrect system οf equatiοns tο sοlve fοr a and c is:

12a + 5c = 169 (equatiοn 1)

22a + 10c = 314 (equatiοn 2)

These equatiοns represent the tοtal ticket sales and revenue οn twο different days.

Tο sοlve this system, we can use the methοd οf eliminatiοn.

-24a - 10c = -338

22a + 10c = 314

-2a = -24

Dividing bοth sides by -2:

a = 12

Nοw we can substitute a = 12 intο equatiοn 1 tο sοlve fοr c:

12(12) + 5c = 169

144 + 5c = 169

5c = 25

c = 5

Therefοre, the cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.

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Answer:

x = 8

Step-by-step explanation:

Let x be the number of blue seats in each section.

Then the total number of seats in each section is:

14 + x

Since there are 4 identical sections, the total number of seats in the theater is:

4(14 + x) = 56 + 4x

We know that the theater has 88 seats, so:

56 + 4x = 88

Simplifying the equation:

4x = 32

x = 8

Therefore, each section has 14 red seats and 8 blue seats.

The expression for the number of blue seats in each section is x = 8.

Answer:

---------------------------------

Let b be the number of blue seats.

There are 4 sections, each has 14 red and b blue seats, with the total number of seats being 88.

The equation to reflect this would be:

Its solution would be:

-3 is not an irrational number, but it is a real number, a rational number, an integer, and a whole number.  

What are whole numbers and rational numbers?

All numbers, including integers, fractions, decimals, and irrational numbers, that can be represented on a number line are considered real numbers.

In summary, real numbers include rational and irrational numbers, and integers include whole number and their negatives.

When two integers are compared, a number can be stated as a ratio, such as -3/1, 1/2, or 5/7. Writing rational numbers as recurring or ending decimals is an option.

Numbers that can't be stated as a ratio of two integers, like 2 or, are referred to as irrational numbers. It is impossible to write irrational numbers using repeating or ending decimals.

Positive and negative whole numbers, as well as zero, are considered integers. Since whole numbers are non-negative integers, they contain zero and only positive values.

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Answer:

To factor completely using the GCMF (Greatest Common Monomial Factor), we first need to identify the common monomial factor of all three terms. In this case, the common monomial factor is 2x²:

10x^5 + 8x^4 - 4x² = 2x²(5x^3 + 4x^2 - 2)

Now, we can see that the expression can be factored further, but it cannot be factored using the GCMF. However, we can use other factoring techniques, such as grouping or factoring by grouping, to factor the remaining expression:

2x²(5x^3 + 4x^2 - 2) = 2x²(5x^3 + 10x^2 - 6x^2 - 2)

= 2x²(5x^2(x + 2) - 2(x + 2))

= 2x²(5x^2 - 2)(x + 2)

Therefore, the expression 10x^5 + 8x^4 - 4x² can be factored completely as 2x²(5x^2 - 2)(x + 2).

Step-by-step explanation:

Answer:

To write Z in Euler form, we first need to find its magnitude and argument.

The magnitude of Z is given by:

|Z| = √(Re(Z)^2 + Im(Z)^2)

where Re(Z) is the real part of Z, and Im(Z) is the imaginary part of Z.

In this case:

Re(Z) = √3

Im(Z) = √3 i

So:

|Z| = √(√3^2 + (√3)^2) = √(3 + 3) = √6

The argument of Z is given by:

arg(Z) = tan^(-1)(Im(Z) / Re(Z))

In this case:

arg(Z) = tan^(-1)((√3) / √3) = tan^(-1)(1) = π/4

Therefore, Z in Euler form is:

Z = |Z| e^(i arg(Z)) = √6 e^(i π/To write Z in Euler form, we first need to find its magnitude and argument.

The magnitude of Z is given by:

|Z| = √(Re(Z)^2 + Im(Z)^2)

where Re(Z) is the real part of Z, and Im(Z) is the imaginary part of Z.

In this case:

Re(Z) = √3

Im(Z) = √3 i

So:

|Z| = √(√3^2 + (√3)^2) = √(3 + 3) = √6

The argument of Z is given by:

arg(Z) = tan^(-1)(Im(Z) / Re(Z))

In this case:

arg(Z) = tan^(-1)((√3) / √3) = tan^(-1)(1) = π/4

Therefore, Z in Euler form is:

Z = |Z| e^(i arg(Z)) = √6 e^(i π/4)

The longest amount of time that Marco could use his phone without changing the battery is given as follows:

3.3 hours.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In 5 hours, the battery fell from 50% to 20%, hence the slope is given as follows:

-30/5 = -6% an hour.

The battery is currently at 20%, hence the time that Marco could use the phone without charging it is given as follows:

20/6 = 3.3 hours.

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Answer:

Let's denote the length, width, and

height of the cuboid as "l", "w", and

"h, respectively. Then, we have:

lw= 24 (Area of one face)

Ih 32 (Area of another face)

wh 48 (Area of the third face)

To solve for the dimensions of the

cuboid, we can use a system of

equations. We can start by solving

for one of the variables in terms of

the other two. For example, from the

first equation, we have:

W 24/

Substituting this into the second

equation, we get:

Ih 32

I(24/)h = 32

24h 32

h 32/24

h 4/3

Next, we can substitute the values of

h and w into the third equation to

solve for:

wh = 48

I(24/)(4/3) = 48

I2 72

= sqrt(72)

I= 6sqrt(2)

Finally, we can use the values of I

and w to solve for the remaining

dimension:

lw 24

(6sqrt(2))(24/(6sqrt(2))) = 24

W = 4sqrt(2)

Therefore, the lengths of the sides of

the cuboid are:

Length () = 6v2 cm

Width (w) = 4/2 cm

Height (h) = 4/3 cm

Answer:

(2, -2)

Step-by-step explanation:

To rotate a point in a coordinate plane 90 degrees clockwise, we need to switch the x and y coordinates and negate the new x coordinate.

So let's apply this formula to the point (-2, -2):

- The new x-coordinate will be the original y-coordinate: -2

- The new y-coordinate will be the negation of the original x-coordinate: -(-2) = 2

Therefore, after rotating (-2, -2) 90 degrees clockwise, we get the point (2, -2).

We can visualize this by plotting both points on a coordinate plane and drawing a line of reflection that represents the rotation:

```

Before rotation:

|

|

|

-------+-------

|

(-2,-2)

After rotation:

|

|

(2,-2)|

-------+-------

|

```

As shown in the diagram above, after rotating (-2,-2) 90 degrees clockwise, it lands at (2,-2).